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Suslin's conjecture on the reduced Whitehead group of a simple algebra
This article has been retracted


Author: Alexander Merkurjev
Journal: J. Amer. Math. Soc.
MSC (2010): Primary 19B99; Secondary 14C25
Published electronically: November 17, 2015
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Abstract:

The article "Suslin's conjecture on the reduced Whitehead group of a simple algebra" by Alexander Merkurjev (electronically published in the Journal of the American Mathematical Society on November 17, 2015) is retracted by the author on April 18, 2016, prior to appearing in an issue, due to mathematical errors detected after publication.

In 1991, A. Suslin conjectured that if the index of a central simple algebra $ A$ is not square-free, then the reduced Whitehead group of $ A$ is nontrivial generically. We prove this conjecture. An immediate application is that the algebraic group $ \mathbf {SL}_1(A)$ of reduced norm $ 1$ elements in such an algebra $ A$ is not a retract rational variety.


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Additional Information

Alexander Merkurjev
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555
Email: merkurev@math.ucla.edu

DOI: https://doi.org/10.1090/jams/850
Received by editor(s): December 8, 2014
Received by editor(s) in revised form: August 7, 2015
Published electronically: November 17, 2015
Additional Notes: The work has been supported by the NSF Grant DMS #1160206 and the Guggenheim Fellowship.
Article copyright: © Copyright 2015 American Mathematical Society

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